Blender Python - Call function when face is newly selected in edit mode?
I couldn't find a way to do this. So I presume there isn't an easy way. But the next best thing is to do add a keymap that triggers when MOUSESELECT is pressed. Here is an example of that.

# store keymaps here to access after registration
addon_keymaps = []

def register():

    # handle the keymap
    wm = bpy.context.window_manager
    km = wm.keyconfigs.addon.keymaps.new(name='Object Mode', space_type='EMPTY')

    kmi = km.keymap_items.new(ObjectCursorArray.bl_idname, 'SPACE', 'PRESS', ctrl=True, shift=True)
    kmi.properties.total = 4

    addon_keymaps.append(km)


def unregister():

    # handle the keymap
    wm = bpy.context.window_manager
    for km in addon_keymaps:
        wm.keyconfigs.addon.keymaps.remove(km)
    # clear the list
    addon_keymaps.clear()`